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http://dx.doi.org/10.4134/JKMS.j190272

EXTENSION OF BLOCK MATRIX REPRESENTATION OF THE GEOMETRIC MEAN  

Choi, Hana (Department of Mathematics Sungkyunkwan University)
Choi, Hayoung (School of Information Science and Technology ShanghaiTech University)
Kim, Sejong (Department of Mathematics Chungbuk National University)
Lee, Hosoo (Department of Mathematics Education Teachers College Jeju National University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.3, 2020 , pp. 641-653 More about this Journal
Abstract
To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: $${\max}\{X:X=X^*,\;\(\array{A&V&X\\V&B&W\\X&W&C}\){\geq}0\}$$. We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.
Keywords
Positive matrix completion; matrix geometric mean; Schur complement;
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